Numerical solutions of elliptic inverse problems via the equation error method

To estimate a parameter in an elliptic boundary value problem, the method of equation error chooses the value that minimizes the error in the PDE and boundary condition (the solution of the BVP having been replaced by a measurement). The estimated parameter converges to the exact value as the measured data converge to the exact value, provided Tikhonov regularization is used to control the instability inherent in the problem. The error in the estimated solution can be bounded in an appropriate quotient norm; estimates can be derived for both the underlying (infinite-dimensional) problem and a finite-element discretization that can be implemented in a practical algorithm. Numerical experiments demonstrate the efficacy and limitations of the method.

Heat transfer in microwave heating

Heat transfer is considered as one of the most critical issues for design and implement of large-scale microwave heating systems, in which improvement of the microwave absorption of materials and suppression of uneven temperature distribution are the two main objectives. The present work focuses on the analysis of heat transfer in microwave heating for achieving highly efficient microwave assisted steelmaking through the investigations on the following aspects: (1) characterization of microwave dissipation using the derived equations, (2) quantification of magnetic loss, (3) determination of microwave absorption properties of materials, (4) modeling of microwave propagation, (5) simulation of heat transfer, and (6) improvement of microwave absorption and heating uniformity. Microwave heating is attributed to the heat generation in materials, which depends on the microwave dissipation. To theoretically characterize microwave heating, simplified equations for determining the transverse electromagnetic mode (TEM) power penetration depth, microwave field attenuation length, and half-power depth of microwaves in materials having both magnetic and dielectric responses were derived. It was followed by developing a simplified equation for quantifying magnetic loss in materials under microwave irradiation to demonstrate the importance of magnetic loss in microwave heating. The permittivity and permeability measurements of various materials, namely, hematite, magnetite concentrate, wüstite, and coal were performed. Microwave loss calculations for these materials were carried out. It is suggested that magnetic loss can play a major role in the heating of magnetic dielectrics. Microwave propagation in various media was predicted using the finite-difference time-domain method. For lossy magnetic dielectrics, the dissipation of microwaves in the medium is ascribed to the decay of both electric and magnetic fields. The heat transfer process in microwave heating of magnetite, which is a typical magnetic dielectric, was simulated by using an explicit finite-difference approach. It is demonstrated that the heat generation due to microwave irradiation dominates the initial temperature rise in the heating and the heat radiation heavily affects the temperature distribution, giving rise to a hot spot in the predicted temperature profile. Microwave heating at 915 MHz exhibits better heating homogeneity than that at 2450 MHz due to larger microwave penetration depth. To minimize/avoid temperature nonuniformity during microwave heating the optimization of object dimension should be considered. The calculated reflection loss over the temperature range of heating is found to be useful for obtaining a rapid optimization of absorber dimension, which increases microwave absorption and achieves relatively uniform heating. To further improve the heating effectiveness, a function for evaluating absorber impedance matching in microwave heating was proposed. It is found that the maximum absorption is associated with perfect impedance matching, which can be achieved by either selecting a reasonable sample dimension or modifying the microwave parameters of the sample.

Reflection, refraction, and rejection : copper smelting heritage and the execution of environmental policy

This dissertation examines the global technological and environmental history of copper smelting and the conflict that developed between historic preservation and environmental remediation at major copper smelting sites in the United States after their productive periods ended. Part I of the dissertation is a synthetic overview of the history of copper smelting and its environmental impact. After reviewing the basic metallurgy of copper ores, the dissertation contains successive chapters on the history of copper smelting to 1640, culminating in the so-called German, or Continental, processing system; on the emergence of the rival Welsh system during the British industrial revolution; and on the growth of American dominance in copper production the late 19th and early 20th centuries. The latter chapter focuses, in particular, on three of the most important early American copper districts: Michigan’s Keweenaw Peninsula, Tennessee’s Copper Basin, and Butte-Anaconda, Montana. As these three districts went into decline and ultimately out of production, they left a rich industrial heritage and significant waste and pollution problems generated by increasingly more sophisticated technologies capable of commercially processing steadily growing volumes of decreasingly rich ores. Part II of the dissertation looks at the conflict between historic preservation and environmental remediation that emerged locally and nationally in copper districts as they went into decline and eventually ceased production. Locally, former copper mining communities often split between those who wished to commemorate a region’s past importance and develop heritage tourism, and local developers who wished to clear up and clean out old industrial sites for other purposes. Nationally, Congress passed laws in the 1960s and 1970s mandating the preservation of historical resources (National Historic Preservation Act) and laws mandating the cleanup of contaminated landscapes (CERCLA, or Superfund), objectives sometimes in conflict – especially in the case of copper smelting sites. The dissertation devotes individual chapters to the conflicts that developed between environmental remediation, particularly involving the Environmental Protection Agency and the heritage movement in the Tennessee, Montana, and Michigan copper districts. A concluding chapter provides a broad model to illustrate the relationship between industrial decline, federal environmental remediation activities, and the growth of heritage consciousness in former copper mining and smelting areas, analyzes why the outcome varied in the three areas, and suggests methods for dealing with heritage-remediation issues to minimize conflict and maximize heritage preservation.

Remote sensing of volcanic plumes using the Advanced Spaceborne Thermal Emission and Reflection Radiometer (ASTER).

The Advanced Spaceborne Thermal Emission and Reflection Radiometer (ASTER) has been used to quantify SO2 emissions from passively degassing volcanoes. This dissertation explores ASTER’s capability to detect SO2 with satellite validation, enhancement techniques and extensive processing of images at a variety of volcanoes. ASTER is compared to the Mini UV Spectrometer (MUSe), a ground based instrument, to determine if reasonable SO2 fluxes can be quantified from a plume emitted from Lascar, Chile. The two sensors were in good agreement with ASTER proving to be a reliable detector of SO2. ASTER illustrated the advantages of imaging a plume in 2D, with better temporal resolution than the MUSe. SO2 plumes in ASTER imagery are not always discernible in the raw TIR data. Principal Component Analysis (PCA) and Decorrelation Stretch (DCS) enhancement techniques were compared to determine how well they highlight a variety of volcanic plumes. DCS produced a consistent output and the composition of the plumes was easy to identify from explosive eruptions. As the plumes became smaller and lower in altitude they became harder to distinguish using DCS. PCA proved to be better at identifying smaller low altitude plumes. ASTER was used to investigate SO2 emissions at Lascar, Chile. Activity at Lascar has been characterized by cyclic behavior and persistent degassing (Matthews et al. 1997). Previous studies at Lascar have primarily focused on changes in thermal infrared anomalies, neglecting gas emissions. Using the SO2 data along with changes in thermal anomalies and visual observations it is evident that Lascar is at the end an eruptive cycle that began in 1993. Declining gas emissions and crater temperatures suggest that the conduit is sealing. ASTER and the Ozone Monitoring Instrument (OMI) were used to determine the annual contribution of SO2 to the troposphere from the Central and South American volcanic arcs between 2000 and 2011. Fluxes of 3.4 Tg/a for Central America and 3.7 Tg/a for South America were calculated. The detection limits of ASTER were explored. The results a proved to be interesting, with plumes from many of the high emitting volcanoes, such as Villarrica, Chile, not being detected by ASTER.

Non-invasive method to predict viscosity and size using total internal reflection fluorescence microscopy (TIRFM) system

This study develops an automated analysis tool by combining total internal reflection fluorescence microscopy (TIRFM), an evanescent wave microscopic imaging technique to capture time-sequential images and the corresponding image processing Matlab code to identify movements of single individual particles. The developed code will enable us to examine two dimensional hindered tangential Brownian motion of nanoparticles with a sub-pixel resolution (nanoscale). The measured mean square displacements of nanoparticles are compared with theoretical predictions to estimate particle diameters and fluid viscosity using a nonlinear regression technique. These estimated values will be confirmed by the diameters and viscosities given by manufacturers to validate this analysis tool. Nano-particles used in these experiments are yellow-green polystyrene fluorescent nanospheres (200 nm, 500 nm and 1000 nm in diameter (nominal); 505 nm excitation and 515 nm emission wavelengths). Solutions used in this experiment are de-ionized (DI) water, 10% d-glucose and 10% glycerol. Mean square displacements obtained near the surface shows significant deviation from theoretical predictions which are attributed to DLVO forces in the region but it conforms to theoretical predictions after ~125 nm onwards. The proposed automation analysis tool will be powerfully employed in the bio-application fields needed for examination of single protein (DNA and/or vesicle) tracking, drug delivery, and cyto-toxicity unlike the traditional measurement techniques that require fixing the cells. Furthermore, this tool can be also usefully applied for the microfluidic areas of non-invasive thermometry, particle tracking velocimetry (PTV), and non-invasive viscometry.